A local measure of symmetry and orientation for individual spikes of grid cells

Weber, Simon; Sprekeler, Henning

doi:10.1371/journal.pcbi.1006804

Cited by 8 publications

(7 citation statements)

References 27 publications

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“…If signals required for grid cell firing are integrated over time, however, such a slow increase is expected. Notably, a similar increase in spatial accuracy of grid cell firing was also reported recently by Weber and Sprekeler, 2019 . Future experimental and computational modeling studies are needed to address the questions whether and how longer integration time windows could support grid cell firing.…”

Section: Discussionsupporting

confidence: 87%

Effects of visual inputs on neural dynamics for coding of location and running speed in medial entorhinal cortex

Dannenberg

Lazaro

Nambiar

et al. 2020

eLife

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Neuronal representations of spatial location and movement speed in the medial entorhinal cortex during the ‘active’ theta state of the brain are important for memory-guided navigation and rely on visual inputs. However, little is known about how visual inputs change neural dynamics as a function of running speed and time. By manipulating visual inputs in mice, we demonstrate that changes in spatial stability of grid cell firing correlate with changes in a proposed speed signal by local field potential theta frequency. In contrast, visual inputs do not alter the running speed-dependent gain in neuronal firing rates. Moreover, we provide evidence that sensory inputs other than visual inputs can support grid cell firing, though less accurately, in complete darkness. Finally, changes in spatial accuracy of grid cell firing on a 10 s time scale suggest that grid cell firing is a function of velocity signals integrated over past time.

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Section: Discussionsupporting

confidence: 87%

Effects of visual inputs on neural dynamics for coding of location and running speed in medial entorhinal cortex

Dannenberg

Lazaro

Nambiar

et al. 2020

eLife

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“…Grid scale is the radius with highest value, averaging over angles. Grid orientation and gridness are determined by first averaging over radial distance and analyzing the sixth component of the Fourier series with respect to angle (Weber and Sprekeler, 2019). The power of this component divided by the total Fourier power measures ‘gridness’ and its complex phase measures the orientation.…”

Section: Methodsmentioning

confidence: 99%

“…By properties of Fourier transforms, truetrue∑normalΦCpol⁢false(normalΦfalse)2 is the total Fourier power, and [∑ΦCpol⁢false(normalΦfalse)]2/Npol is the power of the zeroth component. A similar definition for gridness has been proposed to assign a local grid score to each spike (Weber and Sprekeler, 2019). We use this definition instead of others used in the literature (Stensola et al, 2012) because it has an intuitive meaning as the fraction of angular power contributed by sixfold symmetry to the autocorrelation function.Network grid scales λ, orientations θ, and gridness can be similarly extracted via the network activity autocorrelation functions c⁢false(bold𝐫false).…”

Section: Additional Methodsmentioning

confidence: 99%

A geometric attractor mechanism for self-organization of entorhinal grid modules

Kang

Balasubramanian

2019

eLife

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Grid cells in the medial entorhinal cortex (MEC) respond when an animal occupies a periodic lattice of ‘grid fields’ in the environment. The grids are organized in modules with spatial periods, or scales, clustered around discrete values separated on average by ratios in the range 1.4–1.7. We propose a mechanism that produces this modular structure through dynamical self-organization in the MEC. In attractor network models of grid formation, the grid scale of a single module is set by the distance of recurrent inhibition between neurons. We show that the MEC forms a hierarchy of discrete modules if a smooth increase in inhibition distance along its dorso-ventral axis is accompanied by excitatory interactions along this axis. Moreover, constant scale ratios between successive modules arise through geometric relationships between triangular grids and have values that fall within the observed range. We discuss how interactions required by our model might be tested experimentally.

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“…Grid scale is the radius with highest value, averaging over angles. Grid orientation and gridness are determined by first averaging over radial distance and analyzing the sixth component of the Fourier series with respect to angle [61]. The power of this component divided by the total Fourier power measures "gridness" and its complex phase measures the orientation.…”

Section: Overview Of Data Analysis Techniquesmentioning

confidence: 99%

A geometric attractor mechanism for self-organization of entorhinal grid modules

Kang

Balasubramanian

2018

Preprint

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Grid cells in the medial entorhinal cortex (MEC) respond when an animal occupies a periodic lattice of "grid fields" in the environment. The grids are organized in modules with spatial periods, or scales, clustered around discrete values separated by ratios in the range 1.2-2.0. We propose a mechanism that produces this modular structure through dynamical self-organization in the MEC. In attractor network models of grid formation, the grid scale of a single module is set by the distance of recurrent inhibition between neurons. We show that the MEC forms a hierarchy of discrete modules if a smooth increase in inhibition distance along its dorso-ventral axis is accompanied by excitatory interactions along this axis. Moreover, constant scale ratios between successive modules arise through geometric relationships between triangular grids and have values that fall within the observed range. We discuss how interactions required by our model might be tested experimentally.

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A local measure of symmetry and orientation for individual spikes of grid cells

Cited by 8 publications

References 27 publications

Effects of visual inputs on neural dynamics for coding of location and running speed in medial entorhinal cortex

Effects of visual inputs on neural dynamics for coding of location and running speed in medial entorhinal cortex

A geometric attractor mechanism for self-organization of entorhinal grid modules

A geometric attractor mechanism for self-organization of entorhinal grid modules

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